Microsoft just sent out a notice that Zune Marketplace will no longer support rental and purchase of content, or browsing movies and TV shows, beginning as early as November 22, 2013. This is part of the Fall 2013 update that also retires Microsoft Points for local currency. Remaining Microsoft Points balance are transitioned to local currency when initiating a purchase or redeeming a Microsoft Points card or code on your Xbox 360.
For videos, you can rent and buy the latest movies and TV shows using Xbox Video on Xbox 360, or Windows 8.1 and RT PCs and tablets. You can access Xbox Video on the web and Xbox One console starting November 22nd. Windows Phone 8 devices get it as early as this holiday.
For music, you can purchase your favorite songs and albums using local currency on Windows 8.1 PCs and tablets. No word on Windows Phone 8.
In a similar recent announcement, Microsoft announced that "Xbox Video content you own as of then, will no longer be playable through the Zune PC client, Zune devices, or Windows Phone 7 devices", signaling the further end of Zune.
What will replace all of this Zune functionality for video playback and rental? Microsoft did announce the Xbox Video app coming for Windows Phone, so perhaps the stars will align soon.